Intensive studies have been conducted on fluid-related seismic dispersion and attenuation in saturated anisotropic media. Most of the studies are concentrated on the transversely isotropy media. However, the fractures distribution in subsurface reservoirs is often complex. When there are multiple fracture sets developing in a porous background, the signatures of seismic dispersion and attenuation remain unclear. In this paper, we propose a method to calculate the frequency-dependent stiffness matrix of a porous medium with multiple fractures sets from a perspective of viscoelasticity. Due to the favorable approximation performance of the generalized standard linear solid model and Chapman model, we use a modified form of generalized standard linear solid model to simulate the frequency-dependent stiffness tensor of porous media with multiple fracture sets. The representation of the stiffness tensor utilizes the modulus defect to denote the effects the fractures including fracture density and geometry. With the procedure of calculating the stiffness tensors at low- and high-frequency limits, we can easily calculate the frequency-dependent stiffness tensor for media with multiple fracture sets with arbitrary orientations and directions. We then analyze the effects of the fracture parameters on the viscoelasticity characteristics taking orthotropic medium as an example. The results can help to understand the viscoelasticity and the mesoscopic seismic attenuation associated with fractures and fluids and can provide a practical rock physics model when dealing with reservoirs with complex fracture patterns.
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Ali A, Jakobsen M (2011) Seismic characterization of reservoirs with multiple fracture sets using velocity and attenuation anisotropy data. J Appl Geophys 75(3):590–602. https://doi.org/10.1016/j.jappgeo.2011.09.003
Baird AF, Kendall JM, Angus DA (2013) Frequency-dependent seismic anisotropy due to fractures: fluid flow versus scattering. Geophysics 78(2):WA111–WA122. https://doi.org/10.1190/geo2012-0288.1
Biot MA (1956a) Theory of propagation of elastic waves in fluid-saturated porous solid. I. Low-frequency range. J Acoust Soc Am 28(2):168–178. https://doi.org/10.1121/1.1908239
Biot MA (1956b) Theory of propagation of elastic waves in a fluid-saturated porous solid. II. Higher frequency range. J Acoust Soc Am 28(2):179–191. https://doi.org/10.1121/1.1908241
Brajanovski M, Gurevich B, Schoenberg M (2005) A model for P-wave attenuation and dispersion in a porous medium permeated by aligned fractures. Geophys J Int 163(1):372–384. https://doi.org/10.1111/j.1365-246X.2006.03068.x
Brajanovski M, Müller TM, Parra JO (2010) A model for strong attenuation and dispersion of seismic p-waves in a partially saturated fractured reservoir. Sci Chin Phys Mech Astron 53(8):1383–1387. https://doi.org/10.1007/s11433-010-3205-0
Carcione JM, Gurevich B (2011) Differential form and numerical implementation of Biot’s poroelasticity equations with squirt dissipation. Geophysics 76(6):N55–N64. https://doi.org/10.1190/geo2010-0169.1
Chapman M (2009) Modeling the effect of multiple sets of mesoscale fractures in porous rock on frequency-dependent anisotropy. Geophysics 74(6):D97. https://doi.org/10.1190/1.3204779
Chapman M (2003) Frequency-dependent anisotropy due to meso-scale fractures in the presence of equant porosity. Geophys Prospect 51(5):369–379. https://doi.org/10.1046/j.1365-2478.2003.00384.x
Chapman M, Zatsepin SV, Crampin S (2002) Derivation of a microstructural poroelastic model. Geophys J Roy Astron Soc 151(2):427–451. https://doi.org/10.1046/j.1365-246X.2002.01769.x
Dvorkin J, Mavko G (2006) Modeling attenuation in reservoir and nonreservoir rock. Lead Edge 25(2):194–197. https://doi.org/10.1190/1.2172312
Dvorkin J, Mavko G, Nur A (1995) Squirt flow in fully saturated rocks. Geophysics 60(1):97–107. https://doi.org/10.1190/1.1443767
Galvin R, Gurevich B (2015) Frequency-dependent anisotropy of porous rocks with aligned fractures. Geophys Prospect 63(1):141–150. https://doi.org/10.1111/1365-2478.12177
Gassmann F (1951) Uber die elastizitat poroser Medien. Vier der Natur Gesellschaft in Zurich 96:1–23
Gurevich B, Brajanovski M, Galvin R et al (2009) P-wave dispersion and attenuation in fractured and porous reservoirs-poroelasticity approach. Geophys Prospect 57(2):225–237. https://doi.org/10.1111/j.1365-2478.2009.00785.x
Jakobsen M (2004) The interacting inclusion model of wave-induced fluid flow. Geophys J Int 158(3):1168–1176. https://doi.org/10.1111/j.1365-246X.2004.02360.x
Johnson DL (2001) Theory of frequency dependent acoustics in patchy-saturated porous media. J Acoust Soc Am 110(2):682–694. https://doi.org/10.1121/1.1381021
Lan H (2014) Wave field modelling in fractured porous media and frequency-dependent AVO reservoir parameters inversion. Jinlin University, Jinlin
Maultzsch S, Chapman M, Liu E, Li XY (2003) Modelling frequency-dependent seismic anisotropy in fluid-saturated rock with aligned fractures: implication of fracture size estimation from anisotropic measurements. Geophys Prospect 51(5):381–392. https://doi.org/10.1046/j.1365-2478.2003.00386.x
Mavko G, Nur A (1975) Melt squirt in the asthenosphere. J Geophys Res 80(11):1444–1448. https://doi.org/10.1029/JB080i011p01444
Müller TM, Gurevich B, Lebedev M (2010) Seismic wave attenuation and dispersion resulting from wave-induced flow in porous rocks - a review. Geophysics 75(5):75A147–75A164. https://doi.org/10.1190/1.3463417
Picotti S, Carcione JM, Rubino JG et al (2010) A viscoelastic representation of wave attenuation in porous media. Comput Geosci 36(1):44–53. https://doi.org/10.1016/j.cageo.2009.07.003
Picotti S, Carcione JM (2017) Numerical simulation of wave-induced fluid flow seismic attenuation based on the Cole-Cole model. J Acoust Soc Am 142(1):134–145. https://doi.org/10.1121/1.4990965
Pride SR, Berryman JG (2003a) Linear dynamics of double-porosity dual-permeability materials. I. Governing equations and acoustic attenuation. Phys Rev E 68(3):036603. https://doi.org/10.1103/PhysRevE.68.036603
Pride SR, Berryman JG (2003b) Linear dynamics of double-porosity dual-permeability materials. II. Fluid transport equations. Phys Rev E 68(3):036604. https://doi.org/10.1103/PhysRevE.68.036604
Pride SR, Berryman JG, Harris JM (2004) Seismic attenuation due to wave-induced flow. J Geophys Res Solid Earth. https://doi.org/10.1029/2003JB002639
Rubino JG, Caspari E, Milani M et al (2015) Seismic anisotropy in fractured low-permeability formations: the effects of hydraulic connectivity. Seg Tech Progr Expand. https://doi.org/10.1190/segam2015-5844460.1
Rubino JG, Guarracino L, Müller TM et al (2013) Do seismic waves sense fracture connectivity? Geophys Res Lett 40(4):692–696. https://doi.org/10.1002/grl.50127
Shen B, Siren T, Rinne M (2015) Modelling fracture propagation in anisotropic rock mass. Rock Mech Rock Eng 48(3):1067–1081. https://doi.org/10.1007/s00603-014-0621-x
Shi PD, Yuan SY, Wang TY et al (2018) Fracture identification in a tight sandstone reservoir: a seismic anisotropy and automatic multisensitive attribute fusion framework. IEEE Geosci Remote Sens Lett 15(10):1525–1529. https://doi.org/10.1109/LGRS.2018.2853631
Shuai D, Wei JX, Di BR et al (2017) Experimental study of fracture size effect on elastic-wave velocity dispersion and anisotropy. Geophysics 83(1):1–47. https://doi.org/10.1190/geo2016-0639.1
White JE (1975) Computed seismic speeds and attenuation in rocks with partial gas saturation. Geophysics 40(2):224–232. https://doi.org/10.1190/1.1440520
Yuan SY, LiuY ZZ et al (2019) Prestack stochastic frequency-dependent velocity inversion with rock-physics constraints and statistical associated hydrocarbon attributes. IEEE Geosci Remote Sens Lett 16:140–144. https://doi.org/10.1109/LGRS.2018.2868831
Zhang J, Huang H, Wu C et al (2018) Influence of patchy saturation on seismic dispersion and attenuation in fractured porous media. Geophys J Int 214:583–595. https://doi.org/10.1093/gji/ggy160
Zhu Y, Tsvankin I (2006) Plane-wave propagation in attenuative transversely isotropic media. Geophysics 71(2):T17–T30. https://doi.org/10.1190/1.2187792
National Natural Science Foundation of China (No. 41674139).
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Zhang, J., Ding, R., Zhao, L. et al. Viscoelasticity expression and extension of seismic dispersion and attenuation in porous media with multiple fracture sets. Acta Geophys. (2020). https://doi.org/10.1007/s11600-020-00497-y
- Fractured reservoirs
- Seismic rock physics
- Dispersion and attenuation